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hnaghieh
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- TL;DR Summary
- Is there a relative motion between a moving massive gravitational object with respect to the curved spacetime it produces in its vicinity?
What is Gravitational dragging ?
You mean this?hnaghieh said:What is Gravitational dragging ?
hnaghieh said:I don’t know the mathematics or the phenomenology in terms of what happens to curved spacetime when the massive object moves
Please explain morePeterDonis said:Spacetime is a 4-dimensional geometry that already includes the entire history of the object
hnaghieh said:Please explain more
hnaghieh said:Yes. But I don’t know the mathematics or the phenomenology in terms of what happens to curved spacetime when the massive object moves
PeterDonis said:In the spacetime viewpoint, objects don't "move" and spacetime doesn't "change". Spacetime is a 4-dimensional geometry that already includes the entire history of the object and the spacetime curvature it produces. A spacetime with an object that produces frame dragging simply has a somewhat different geometry from a spacetime with an object that doesn't.
but a moving charge creates a magnetic or electric field when it moves through a medium. If the medium moves with the charge no effect can be found.pervect said:Mathematically, frame-dragging is rather similar to the way that a moving charge creates a magnetic field as well as an electric one.
No it doesn't - there's no medium for electromagnetic fields. The supposed "ether" was found inconsistent with experiment over a century ago.hnaghieh said:but a moving charge creates a magnetic or electric field when it moves through a medium.
I apologize for not being careful when I said medium. I meant “field”. Lorentz force; if a charged particle q moves with velocity v in the presence of an electric field E and a magnetic field B then it will experience a force F. If no velocity no force. Do you agree?Ibix said:No it doesn't - there's no medium for electromagnetic fields. The supposed "ether" was found inconsistent with experiment over a century ago.
Peter's point was that spacetime can't change with time because time is just a direction in spacetime. You can imagine 'slicing' 4d spacetime into 3d 'sheets' which are each all of space at a single time. These sheets may have different geometries, but that's not because anything is being "dragged around" by mass.
So do you mean these 3D sheets at a single time (hypersurfaces?) which have a specific flat local metric do not change with the presence of a massive object from point to point either according to world postulate(world line) or according to Einstein’s “ mollusk”?Ibix said:Peter's point was that spacetime can't change with time because time is just a direction in spacetime. You can imagine 'slicing' 4d spacetime into 3d 'sheets' which are each all of space at a single time. These sheets may have different geometries, but that's not because anything is being "dragged around" by mass.
Not if the electric field is non-zero. And you seem to be positing a particle having a velocity with respect to the field. This is no such thing. The velocity in the Lorentz force equation is the velocity with respect to the reference frame in which the field is measured.hnaghieh said:Do you agree?
I didn't say they were flat. They won't be in general. And no, they cannot change because they aren't equipped with a notion of time. You can compare one slice to another at a later time (with some care, there are a lot of traps for the unwary) and they may have a different geometry, yes.hnaghieh said:So do you mean these 3D sheets at a single time (hypersurfaces?) which have a specific flat local metric do not change with the presence of a massive object from point to point either according to world postulate(world line) or according to Einstein’s “ mollusk”?
No. One component of the force is ##q\vec{E}##, which is independent of velocity.hnaghieh said:If no velocity no force. Do you agree?
We can speak of an object's position in space changing over time - that's what we mean by "moving". However, this situation is represented in four-dimensional spacetime by a stationary curve - nothing moves or changes.hnaghieh said:Please explain more
“Stationary curve”in what? Relative to what frame of reference is this curve stationary and what is the definition of “stationary”? A photons trajectory is can be straight line or curved depending on the chosen frame. But how do you explain it’s motion from Big Bang and across universe? Please help with more explainingNugatory said:We can speak of an object's position in space changing over time - that's what we mean by "moving". However, this situation is represented in four-dimensional spacetime by a stationary curve - nothing moves or changes.
If a charged particles velocity is parallel to the magnetic field, then there is no net force and the particle moves in a straight lineNugatory said:No. One component of the force is ##q\vec{E}##, which is independent of velocity.
I am trying to understand this “week effect “. What is it’s mechanism ? How does it affect a free falling object in the curved space time in the vicinity of a massive object. How are the hypersurfaces of that space time affected. How are these effects communicated throughout the spacetime. I apologize for asking Too many questions.pervect said:It's a pretty weak effect though. Gravity probe B detected the frame dragging due to the Earth's rotation, which provides a field analogous to that of a spinning charge. However, this effect is tiny, it took extrodinary measures to be able to detect it for the rotating Earth.
hnaghieh said:If a charged particles velocity is parallel to the magnetic field, then there is no net force and the particle moves in a straight line
I agree.PeroK said:Not if there is an electric field. See, for example:
http://farside.ph.utexas.edu/teaching/em/lectures/node33.html
If I may add that my original question included Linear motion as well as rotational motion dragging which gravity probe B detected.hnaghieh said:I am trying to understand this “week effect “. What is it’s mechanism ? How does it affect a free falling object in the curved space time in the vicinity of a massive object. How are the hypersurfaces of that space time affected. How are these effects communicated throughout the spacetime. I apologize for asking Too many questions.
A curve in spacetime.hnaghieh said:“Stationary curve”in what?
You are misunderstanding @Nugatory's use of "stationary". He just means that the curve is a curve in spacetime. It can't change. The notion of change is just where the path goes in spacetime.hnaghieh said:Relative to what frame of reference is this curve stationary and what is the definition of “stationary”?
Objects are modeled as a bundle of paths in spacetime, and what you probably think of as an object is a 3d slice through that bundle.hnaghieh said:Please help with more explaining
Unless there is an electric field, as has been pointed out multiple times now.hnaghieh said:If a charged particles velocity is parallel to the magnetic field, then there is no net force and the particle moves in a straight line
Spacetime is a curved manifold. Depending on the geometry, which depends on the distribution of stress-energy, the geodesic paths (the curved manifold equivalent of straight lines) are different. And free-falling objects follow geodesics.hnaghieh said:I am trying to understand this “week effect “. What is it’s mechanism ?
hnaghieh said:these 3D sheets at a single time (hypersurfaces?) which have a specific flat local metric do not change
Imagine freely falling test particles toward a mass (a planet, a star, ...). Then there are two cases, the mass ishnaghieh said:I am trying to understand this “week effect “. What is it’s mechanism ? How does it affect a free falling object in the curved space time in the vicinity of a massive object.
timmdeeg said:the trajectory of the particles is slightly bent in the direction of the rotation.
“Rotating” or “not rotating” against what? What is the frame of reference with respect to which the mass is rotating (or not)? Other stars? Microwave back ground? The space time itself?timmdeeg said:a) not rotating: the trajectory of the particles is a straight line towards the center of the mass.
b) rotating: the trajectory of the particles is slightly bent in the direction of the rotation.
hnaghieh said:“Rotating” or “not rotating” against what?
Any observer at rest with respect with the center of mass of the massive object by definition is rotating (moving) with that object unless it is non-rigidly connected with that massive object.PeterDonis said:With respect to an observer at infinity who is at rest with respect to the center of mass of the massive object.
That rest frame observer will not be able to determine the state of motion of the massive object from within its rest frame. However , a stationary observer (not moving with the center of the mass of the massive object hence one who has a relative velocity with respect to the massive object) will be able to determine a relative velocity. Which bring us to the original question. Do moving object carry/ drag the curved spacetime in their vicinity?hnaghieh said:Any observer at rest with respect with the center of mass of the massive object by definition is rotating (moving) with that object unless it is non-rigidly connected with that massive object.
Do not confuse rotating and moving. Rotation is not relative - it can be measured with an accelerometer without reference to anything external or requirement to choose any particular reference frame. Frame dragging will happen in the vicinity of a rotating object.hnaghieh said:Which bring us to the original question. Do moving object carry/ drag the curved spacetime in their vicinity?
I put moving in the bracket to indicate that a rest frame observer with respect to the center of the mass of the massive object, moves by definition with the center of the mass whether it’s rotating or linearly moving.Nugatory said:Do not confuse rotating and moving
I feel that my original question is analogous to the question that started it all in the 19th century and led to Michelson and Morley experiment of course with different terminology. They asked if there was a relative motion between the Earth and the ether. Gravity probe B asked if there was a frame dragging (linear or rotational) by massive objects. And I am not suggesting that ether exists or that curved spacetime is ether. But are we not trying to find the same thing in reverse ? Namely the rotation of curved spacetime with respect to Earth from within the rest frame of the earth?hnaghieh said:I put moving in the bracket to indicate that a rest frame observer with respect to the center of the mass of the massive object, moves by definition with the center of the mass whether it’s rotating or linearly moving.
hnaghieh said:Any observer at rest with respect with the center of mass of the massive object by definition is rotating (moving) with that object unless it is non-rigidly connected with that massive object.
hnaghieh said:Gravity probe B asked if there was a frame dragging (linear or rotational) by massive objects.
No, a moving charge in vacuum has always its electromagnetic field around it as described by the "microscopic" Maxwell equations.hnaghieh said:but a moving charge creates a magnetic or electric field when it moves through a medium. If the medium moves with the charge no effect can be found.